Late-September through early-October is a great time to visit the Oregon Coast for outdoor recreation and wildlife spotting. With the large summer crowds gone, herds of Roosevelt Elk are frequently seen along the coast. If you’re interested in whale watching, I’d suggest Depoe Bay, where Oregon State Parks operates a Whale Watch Center, or Cape Foulweather, a prominent viewpoint also staffed by Parks personnel. Bird watching is always good on the Oregon Coast. You may want to read my Travel Oregon story, Hiking Tour of the Oregon Coast, for some of my favorite hiking areas.
September 24 is National Public Lands Day and National Parks, such as Lewis and Clark’s Fort Clatsop near Astoria, offer free admission in case that fits in with your itinerary. That day is also Oregon’s annual Beach Clean-up in case you want to join the thousands of other volunteers helping keep Oregon’s beaches clean. On October 1-2, the town of Charleston hosts its Octoberfish festival. That weekend, Lincoln City hosts its annual Fall Kite Festival. You can see more events at the VisitTheOregonCoast website
As for arts, there are some great galleries and live theater all along the Coast, but Cannon Beach in particular is known as an arts town and has been recognized as one the 100 Best Art Towns in America.
If you give me an idea of your itinerary or what part of the coast you will be visiting, I may be able to make some more specific recommendations.